Subgroups — #17992578

Order 4736.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596925	C₂	1	1	yes	maximal, characteristic
2	#14557309	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#446	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596925	—	2	1	no	—
5	C₂×#10596925	—	2	1	no	—
6	C₄×Q₈×C₃₇	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₃₇	—	2	1	no	—
8	C₄⋊C₈×C₃₇	C₄	1	1	yes	characteristic
9	#97×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₃₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₇	—	2	1	no	—
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₃₇	—	2	1	no	—
16	C₄⋊C₄×C₃₇	C₈	1	1	yes	characteristic
17	C₄²×C₃₇	—	2	1	no	—
18	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
19	#10596925	—	2	2	no	—
20	#10596925	—	4	1	no	—
21	Q₈×C₃₇	—	4	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
27	C₈×C₃₇	—	2	1	no	—
28	C₈×C₃₇	—	4	1	no	—
29	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
31	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₃₇	—	2	1	no	—
33	C₄×C₃₇	—	2	1	no	—
34	C₄×C₃₇	—	4	1	no	—
35	C₄×C₃₇	—	4	1	no	—
36	C₄×C₃₇	#103	1	1	yes	characteristic
37	C₄×C₃₇	#104	1	1	yes	characteristic
38	#1338	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	Q₈⋊C₈	1	1	yes	characteristic
40	C₂×C₃₇	#349	1	1	yes	characteristic
41	C₂×C₃₇	#350	1	1	yes	characteristic
42	#446	D₃₇	1	1	yes	characteristic
43	C₄⋊C₁₆	—	37	1	no	—
44	#346	—	37	1	no	—
45	C₃₇	#1338	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₈	Dic₃₇	1	1	yes	characteristic
47	C₂×C₁₆	—	74	1	no	—
48	C₂×C₁₆	—	74	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄⋊C₈	Dic₃₇	1	1	yes	characteristic
51	#97	—	2	1	no	—
52	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
53	C₂×Q₈	#64436	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	#64436	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
61	C₁₆	—	74	2	no	—
62	C₁₆	—	148	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂×#64436	1	1	yes	characteristic
67	C₂×C₄	#10596934	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊Dic₃₇	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	4	1	no	—
71	C₈	#10596941	1	1	yes	characteristic
72	C₈	#10596942	1	1	yes	characteristic
73	C₂²	C₂²⋊#64436	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#11924460	1	1	yes	characteristic
79	C₄	#11924463	1	1	yes	characteristic
80	C₂	Q₈⋊#64436	1	1	yes	characteristic
81	C₂	#14557315	1	1	yes	characteristic
82	C₂	#14557317	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₃₇
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#446	C₂
socle, prime radical	C₂²×C₃₇	C₂²⋊C₈
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#446	D₃₇
hypocenter	C₃₇	#1338
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #446

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
45. C₃₇	#1338	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄⋊#10596925	2
#14557309	2
C₃₇×#446	2
#1338	37